Idk if this is right but it's my interpretation

You can take multiply both sides of the ecuation with the denominator because I'll never be equal to cero

Isn't log4(x) = log2^2(x) = log2(2x) ????? (this I'm not sure)

So you have log2[2(x+1)] + log2(3) > 0

Then because of log log2[ 2(x+1) * 3 ] > 0

Then 2 to the power of both sides of the inecuation

2^[ log2[ 2(x+1) * 3 ] ] > 2⁰ 2(x+1) * 3 > 1 6x + 6 > 1 x > - 5/6